In this paper, we extend our previous work on a goal-oriented inverse design method to carry out inverse robust design by managing the uncertainty involved. The extension embodies the introduction of specific robust design goals and new robust solution constraints anchored in the mathematical constructs of Error Margin Indices (EMIs) and Design Capability Indices (DCIs) to determine “satisficing” robust design specifications across analytical model-based process chains. Contributions in this paper include the designer’s ability to explore satisficing robust solution regions when multiple conflicting goals and multiple sources of uncertainty are present. Using the goal-oriented inverse design method, robust solutions are propagated in an inverse manner. We demonstrate the efficacy of the method and the associated robust design functionalities using an industry-inspired hot rolling and cooling process chain example problem for the production of a steel rod. In this example, we showcase the formulation of multiple mechanical property goals for the end product using the robustness metrics and the exploration of satisficing robust solutions for material microstructure after the cooling process using the robust solution constraints. The robust solutions thus identified are communicated in an inverse manner using the design method to explore satisficing robust solutions for the microstructure generated after the hot rolling process. Using the example, we demonstrate the robust co-design of material, product, and associated manufacturing processes. The method and the associated design constructs are generic and support the formulation and inverse robust design exploration under uncertainty of similar problems involving a sequential, analytical model-based flow of information across process chains.